On the convergence properties of measurable multifunctions with values in a separable Banach space |
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Authors: | Nikolaos S Papageorgiou |
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Institution: | 1. Department of Mathematics, National Technical University, 1573, Attens, Greece
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Abstract: | In this paper we prove some convergence theorems for Banach space valued multifunctions. First we consider the notion of weak
convergence of sets and prove a weak completeness and a weak compactness result of the Dunford-Pettis type for weakly compact,
convex valued integrable multifunctions. Then we consider set valued martingales and establish two convergence theorems. One
using the Kuratowski-Mosco mode of convergence and for the other the Hausdorff mode. |
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Keywords: | Weak convergence of sets set valued martingale set valued Radon-Nikodym derivative Kuratowski-Mosco convergence support function Hausdorff metric |
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